Question

For a polynomial function y = f(x):
f(x) > 0 when 1 < x < 3 or x > 3 and f(x) < 0 when x < –2 or –2 < x < 1

a) Write a possible equation for this function.

b) Is it possible to find a unique equation for this polynomial function with given information? Explain your answer using as much detail as possible.

Answer 1

Instead of crossing the x-axis when x = -2 or 3, it just touches it, so there are double roots there.

y = (x+2)^2 (x-1) (x-3)^2

there is no unique equation, since all we know are the zeroes. Any multiple of this product of factors will work.